Problem: $A$ $B$ $C$ If: $ AB = 7x + 3$, $ AC = 117$, and $ BC = 5x + 6$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {7x + 3} + {5x + 6} = {117}$ Combine like terms: $ 12x + 9 = {117}$ Subtract $9$ from both sides: $ 12x = 108$ Divide both sides by $12$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $BC$ $ BC = 5({9}) + 6$ Simplify: $ {BC = 45 + 6}$ Simplify to find ${BC}$ : $ {BC = 51}$